The Bitcoin protocol is essentially a mathematical algorithm operating on a decentralized network, managing transaction data and achieving consensus among participants. If a majority of participants are honest, then automatic consensus is reached. With decentralization as its main feature, there is no central authority in control. Individuals in the network are voluntary participants with equal rights and responsibilities, and the network is open for anyone to join. Since its launch in January 2009, the network has been resilient and unstoppable, functioning continuously without significant interruptions.

The code and development of Bitcoin are open and have been used as the basis for numerous other cryptocurrencies. The network’s security relies heavily on advanced cryptography, such as hash functions (SHA256, RIPEMD-160) and the elliptic curve digital signatures algorithm (ECDSA). While the cryptography utilized is widely known and standardized, ongoing research explores unique cryptographic features of other cryptocurrencies.

In the Bitcoin network, nodes represent the program running on different machines communicating with each other. Transactions are validated, broadcasted, and checked continuously by nodes following strict rules. Incentives are in place to penalize any deviations from the rules, creating a self-regulating system. The network operates as a complex Dynamical System, with stability posing an intriguing mathematical problem involving functions, martingale theory, Markov chains, Dyck words, and more.

Transactions are broadcasted and validated by nodes in the network, with the validation process known as mining. Mining involves the creation of new Bitcoin, incentivizing nodes to participate in the validation process.